Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 160 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.28.0

Kron map of kron state

MatrixMap.kron_map_of_kron_state

Plain-language statement

The operational definition of the Kronecker product MatrixMap.kron, that it maps a Kronecker product of inputs to the Kronecker product of outputs. It is the unique bilinear map doing so.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Module Basis to Dual Equiv symm comp dual Map to Dual Equiv

MatrixMap.Module.Basis.toDualEquiv_symm_comp_dualMap_toDualEquiv

Plain-language statement

The composition of the inverse of the dual basis isomorphism with the dual of the dual basis isomorphism is the inverse of the evaluation map.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Entropy A eq entropy Z

MicroHamiltonian.entropy_A_eq_entropy_Z

Plain-language statement

The two definitions of entropy, in terms of T or β, are equivalent.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Mixed convex roof of pure

mixed_convex_roof_of_pure

Plain-language statement

The mixed convex roof extension of f : MState d → ℝ≥0 applied to a pure state ψ is f (pure ψ).

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

Fidelity self eq one

MState.fidelity_self_eq_one

Plain-language statement

A state has perfect fidelity with itself.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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